Beyond Capacity: The Joint Time-Rate Region

TL;DR

This paper introduces the time-rate region, a generalization of capacity in network communication, allowing different receivers to decode information at different times, with an inner-bound derived through reduction to standard capacity.

Contribution

It extends traditional capacity concepts by defining and analyzing the time-rate region, accommodating asynchronous decoding times in network communication.

Findings

Inner-bound on the time-rate region established

Reduction to standard capacity used for analysis

Generalizes static broadcasting to broader scenarios

Abstract

The traditional notion of capacity studied in the context of memoryless network communication builds on the concept of block-codes and requires that, for sufficiently large blocklength n, all receiver nodes simultaneously decode their required information after n channel uses. In this work, we generalize the traditional capacity region by exploring communication rates achievable when some receivers are required to decode their information before others, at different predetermined times; referred here as the "time-rate" region. Through a reduction to the standard notion of capacity, we present an inner-bound on the time-rate region. The time-rate region has been previously studied and characterized for the memoryless broadcast channel (with a sole common message) under the name "static broadcasting".